1. Field of the Invention
The present invention relates to a phase-locked loop (PLL) and, more particularly, to a frequency synthesis system with self-calibrated loop stability and bandwidth.
2. Description of Related Art
In wireless receiving systems, a widely adaptive frequency synthesizer for television receivers, WiMax receivers and the like is a tough challenge on design. For each output frequency of the frequency synthesizer, the parameters (such as the frequency of an input signal, a multiplication factor, etc.) have to be accurately adjusted for minimizing the phase noises and maintaining the stability of the frequency synthesizer.
In the frequency synthesizer, the loop bandwidth indicates the response speed, and preferably is 1/20 of the reference frequency. The damping factor indicates the stability of the frequency synthesizer, and preferably is close to one. The systematic parameters above are related to special circuit parameters such as a charge pump current and the resistance of a filter. Therefore, the loop bandwidth and the damping factor will be varied with input/output frequencies, multiplication factors, and the like.
The various output frequencies and multiplication factors lead to different PLLs on design for different applications. Such a way increases complication in management and also development cost for different PLL designs and tests. A solution for this problem is to apply a complicated circuit and algorithm in one PLL to meet the various output frequencies and the multiplication factors. Namely, a single PLL is designed and applied in different ICs. In such a design, the loop bandwidth and the damping factor require an automatic tuning mechanism to meet with various input frequencies, output frequencies and multiplication factors in different applications.
The parameters of an adaptive PLL can be adjusted to meet the desired output frequencies and multiplication factors. The adaptive PLL can reach to a fixed bandwidth to reference frequency ratio and a fixed damping factor, independent of processes, applied voltages and temperatures. Such features allow the bandwidth to be a fraction of a designed reference frequency, and the fraction is adjusted to reduce the phase noises of the voltage controlled oscillator (VCO), thereby optimizing the output phase noises of the adaptive PLL.
FIG. 1 is a block diagram of a typical PLL 100. In FIG. 1, the PLL 100 includes a phase detector 110, a charge pump 120, a filter 130, a VCO 140 and a frequency divider 150. When the PLL 100 is locked, the frequency of the signal CKOUT produced by the PLL 100 is N times of the frequency of the reference signal CKREF.
FIG. 2 is a block diagram of a typical PLL 100 in phase domain. As shown in FIG. 2, in phase domain, the phase detector 110, the charge pump 120 and the filter 130 can be equivalent to Kd·KF·F(S), and the VCO 140 can be equivalent to
            K              V        ⁢                                  ⁢        C        ⁢                                  ⁢        O              s    ,where ΦO indicates phase of the output signal CKOUT and ΦI indicates phase of the reference signal CKREF. Accordingly, the transfer function
      Φ    O        Φ    I  can be expressed as:
                              Δ          ⁢                                          ⁢                      Φ            ⟶            Δ                    ⁢                                          ⁢                                    I              CH                        ⟶            Δ                    ⁢                                          ⁢                                    V              ϕ                        ⟶            Δ                    ⁢                                          ⁢                      f            ⟶            Δ                    ⁢                                          ⁢          Φ                ⁢                                  ⁢                                            Φ              O                        =                                                                                                      (                                                                        Φ                          I                                                -                                                                              Φ                            O                                                    N                                                                    )                                                              ︸                                              Δ                        ⁢                                                                                                  ⁢                        Φ                                                                              ·                                      I                    CH                                    ·                                                            (                                              R                        +                                                  1                          sC                                                                    )                                                              ︸                                              F                        ⁡                                                  (                          S                          )                                                                                                      ·                                      K                                          V                      ⁢                                                                                          ⁢                      C                      ⁢                                                                                          ⁢                      O                                                        ·                                      1                    s                                                  ⁢                                                                  ⇒                                                      Φ                    O                                    ⁡                                      (                                          1                      +                                                                                                    I                            CH                                                    N                                                ·                                                                              F                            ⁡                                                          (                              S                              )                                                                                s                                                ·                                                  K                                                      V                            ⁢                                                                                                                  ⁢                            C                            ⁢                                                                                                                  ⁢                            O                                                                                                                )                                                              =                                                                                          Φ                      I                                        ·                                          I                      CH                                        ·                                                                  F                        ⁡                                                  (                          S                          )                                                                    s                                        ·                                          K                                              V                        ⁢                                                                                                  ⁢                        C                        ⁢                                                                                                  ⁢                        O                                                                              ⁢                                                                          ⇒                                                            Φ                      O                                                              Φ                      I                                                                      =                                                                                                    I                        CH                                            ·                                                                        F                          ⁡                                                      (                            S                            )                                                                          s                                            ·                                              K                                                  V                          ⁢                                                                                                          ⁢                          C                          ⁢                                                                                                          ⁢                          O                                                                                                            1                      +                                                                                                    I                            CH                                                    N                                                ·                                                                              F                            ⁡                                                          (                              S                              )                                                                                s                                                ·                                                  K                                                      V                            ⁢                                                                                                                  ⁢                            C                            ⁢                                                                                                                  ⁢                            O                                                                                                                                =                                                                                                              I                          CH                                                ·                                                                              1                            +                            sRC                                                                                                              s                              2                                                        ·                            C                                                                          ·                                                  K                                                      V                            ⁢                                                                                                                  ⁢                            C                            ⁢                                                                                                                  ⁢                            O                                                                                                                      1                        +                                                                                                            I                              CH                                                        N                                                    ·                                                                                    1                              +                              sRC                                                                                                                      s                                2                                                            ·                              C                                                                                ·                                                      K                                                          V                              ⁢                                                                                                                          ⁢                              C                              ⁢                                                                                                                          ⁢                              O                                                                                                                                            ⁢                                                                                  =                                                                                                                                                                                                                        I                                  CH                                                                ·                                                                  (                                                                      1                                    +                                    sRC                                                                    )                                                                ·                                                                                                                                                                                                        K                                                                  V                                  ⁢                                                                                                                                          ⁢                                  C                                  ⁢                                                                                                                                          ⁢                                  O                                                                                                                                                                                                                                                                                                                                                              s                                    2                                                                    ⁢                                  C                                                                +                                                                                                                                            I                                      CH                                                                        N                                                                    ·                                                                      K                                                                          V                                      ⁢                                                                                                                                                          ⁢                                      C                                      ⁢                                                                                                                                                          ⁢                                      O                                                                                                                                      +                                                                                                                                                                                                        s                                ·                                                                                                      I                                    CH                                                                    N                                                                ·                                RC                                ·                                                                  K                                                                      V                                    ⁢                                                                                                                                                  ⁢                                    C                                    ⁢                                                                                                                                                  ⁢                                    O                                                                                                                                                                                                                          =                                                                                                                                                                                                                                                                              I                                      CH                                                                        ·                                                                          K                                                                              V                                        ⁢                                                                                                                                                                  ⁢                                        C                                        ⁢                                                                                                                                                                  ⁢                                        O                                                                                                                                              +                                                                                                            I                                      CH                                                                        ·                                                                                                                                                                                                                                                        sRC                                  ·                                                                      K                                                                          V                                      ⁢                                                                                                                                                          ⁢                                      C                                      ⁢                                                                                                                                                          ⁢                                      O                                                                                                                                                                                                                                                                                                                                                                                                                          s                                      2                                                                        ⁢                                    C                                                                    +                                                                                                                                                    I                                        CH                                                                            N                                                                        ·                                                                          K                                                                              V                                        ⁢                                                                                                                                                                  ⁢                                        C                                        ⁢                                                                                                                                                                  ⁢                                        O                                                                                                                                              +                                                                                                                                                                                                                                                                                                I                                      CH                                                                        N                                                                    ·                                  sRC                                  ·                                                                      K                                                                          V                                      ⁢                                                                                                                                                          ⁢                                      C                                      ⁢                                                                                                                                                          ⁢                                      O                                                                                                                                                                                                                                          ⁢                                                                                                  =                                                                              N                            ·                                                                                          1                                +                                sRC                                                                                                                                                                                                        1                                      +                                      sRC                                      +                                                                                                                        s                                          2                                                                                ·                                                                                                                                                                                                                                                                                        NCI                                      ⁡                                                                              (                                                                                                                              I                                            CH                                                                                    ·                                                                                      K                                                                                          V                                              ⁢                                                                                                                                                                                          ⁢                                              C                                              ⁢                                                                                                                                                                                          ⁢                                              O                                                                                                                                                                      )                                                                                                                                                                                                                                                          =                                                      N                            ⁢                                                                                          1                                +                                                                  2                                  ·                                  ϛ                                  ·                                                                      (                                                                          s                                      /                                                                              ω                                        n                                                                                                              )                                                                                                                                                              1                                +                                                                  2                                  ·                                  ϛ                                  ·                                                                      (                                                                          s                                      /                                                                              ω                                        n                                                                                                              )                                                                                                  +                                                                                                      (                                                                          s                                      /                                                                              ω                                        n                                                                                                              )                                                                    2                                                                                                                                                                                                                                                                      ,                                    (        1        )            where ωn and ζ can be expressed as:
                                          ω            n                    =                                                                      I                  CH                                ·                                  K                                      V                    ⁢                                                                                  ⁢                    C                    ⁢                                                                                  ⁢                    O                                                                              N                ·                C                                                    ⁢                                  ⁢                              ϛ            =                                          1                2                            ⁢                                                                    1                    N                                    ⁢                                                            I                      CH                                        ·                                          K                                              V                        ⁢                                                                                                  ⁢                        C                        ⁢                                                                                                  ⁢                        O                                                                              ⁢                                                            R                      2                                        ·                    C                                                                                ,                                    (        2        )            for ωn indicates the loop bandwidth and ζ indicates the damping factor. In a typical application, ICH is in proportion to N in order to reduce the affection of N change. However, a PLL product typically requires a constant loop bandwidth
      ω    n        ω    REF  and a constant damping factor ζ. From equation (2), it is known that
      ω    n        ω    REF  is not a constant, and the loop bandwidth ωn and the damping factor ζ are a function of the circuit parameters of the PLL 100. Thus, the constant loop bandwidth
      ω    n        ω    REF  and the constant damping factor ζ shown in equation (2) cannot meet with the constant requirement for different applications.
Therefore, it is desirable to provide an improved frequency synthesis system to mitigate and/or obviate the aforementioned problems.